ROE means return on equity and is a performance measure.
It is a combination (in the classic DuPont formula) of ROA and the leverage ratio, or decomposed:
ROE = ROA * Leverage Ratio = Net income/Total Avg Assets * Total Avg Assets/Total Avg Equity = Net income/Sales * Sales/Total Avg Assets * Total Avg Assets/Total Avg Equity
As a performance measure, ROE tells you how efficiently profits are generated by each dollar of equity invested.
This measure relies upon the accrual accounting system.
For example, banks typically have very low ROA (because of huge asset base generated via deposits) but competitive ROE (deposits create leverage).
So whereas they may only earn $1 for every $100 of assets (1%), they could still earn a 10% RoE (because shareholder equity is only $10).
ROI is the rate of return, over some period of time.
Unless specified, it should be calculated relative to every dollar invested (aka total capital).
The measure relies upon actual cashflows.
Continuing with the previous example, if the bank shareholder bought his share of stock for $10/share and the bank paid dividends of $0.50 per annum, and then the shareholder sold his stock two years later for $13.40, the ROI would be calculated from:
($0.50 + $0.50 + $13.40) = $10(1+r)^2
Where r is the annual rate of return.
In this case, r is 20%.
However, the ROE of the bank might still be 10% based on book value measures.
Furthermore, the actual ROI of the bank (not that individual shareholder) would be different since one has to account for both equity and debt holders.
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